{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Doyle-Fuller-Newman Model with particle-size distributions"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook demonstrates the extension of the Doyle-Fuller-Newman (DFN) model to include a distribution of particle sizes at every macroscale location (e.g. through-cell coordinate $x$) within the electrodes. This model, referred to here as the Many-Particle DFN (or MP-DFN), also extends the ideas of the Many-Particle Model or MPM (an $x$-averaged model) into the DFN framework. Note: this differs from a \"size distribution in x\", where the particle size is a function of $x$ but with only a single size at any given value of $x$.\n",
    "\n",
    "The [MPM notebook](https://github.com/pybamm-team/PyBaMM/blob/develop/docs/source/examples/notebooks/models/MPM.ipynb) describes how the particle-size distributions are implemented in PyBaMM, and how to input parameters and plot some relevant output variables. The model equations for the MP-DFN, which allow for variations in the through-cell $x$ direction and therefore include electrolyte dynamics, are similar to those of the MPM and DFN, and are available in [[5]](#References).\n",
    "\n",
    "By default per electrode, the DFN has 1 microscale dimension (the radial coordinate within the active particles, $r_{\\mathrm{k}}$, $\\mathrm{k}=\\mathrm{n,p}$) and 1 macroscale dimension (the through-cell coordinate $x$), and is commonly called \"pseudo-2D\". The MP-DFN adds another microscale variation with particle size $R_{\\mathrm{k}}$, $\\mathrm{k}=\\mathrm{n,p}$ over an interval $[R_{\\mathrm{k,min}}, R_{\\mathrm{k,max}}]$, $\\mathrm{k}=\\mathrm{n,p}$, and thus can be thought of as \"pseudo-3D\". See [[5]](#References) for more details. "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example solving the MP-DFN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install \"pybamm[plot,cite]\" -q    # install PyBaMM if it is not installed\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import pybamm"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The MP-DFN can be accessed from the `DFN` model in PyBaMM, and specifying the `\"particle size\"` option. The default option for `\"particle size\"` is `\"single\"`. Let's change this to `\"distribution\"` and pass to the `DFN` when loading the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# choose option(s)\n",
    "options = {\"particle size\": \"distribution\"}\n",
    "\n",
    "# load model\n",
    "model = pybamm.lithium_ion.DFN(options=options, name=\"MP-DFN\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adding size distribution parameters"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now need to input and set the particle-size distributions and the minimum and maximum sizes for each electrode. Values for these are not currently in the default parameter set for the DFN, but they are easily added (to any parameter set of choice) - see the [MPM notebook](https://github.com/pybamm-team/PyBaMM/blob/develop/docs/source/examples/notebooks/models/MPM.ipynb) for more details.\n",
    "\n",
    "Here, we start from the Marquis et al. (2019) [[6]](#References) parameter set and use the convenience method `pybamm.get_size_distribution_parameters()`, which adds lognormals for the area-weighted size distribution in each electrode. By default, it chooses the `\"Negative particle radius [m]\"` and `\"Positive particle radius [m]\"` values already in the parameter set to be the mean of the lognormals, and sets the standard deviations to be 0.3 times the mean. (All parameters can be overwritten with keyword arguments.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Base parameter set (no distribution parameters by default)\n",
    "params = pybamm.ParameterValues(\"Marquis2019\")\n",
    "\n",
    "# Add distribution parameters to the set, with default values (lognormals)\n",
    "params = pybamm.get_size_distribution_parameters(params)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solve for a 1C discharge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pybamm.solvers.solution.Solution at 0x7fd4e17c43a0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# load parameter values into simuluation\n",
    "sim = pybamm.Simulation(model, parameter_values=params)\n",
    "\n",
    "# solve\n",
    "sim.solve(t_eval=[0, 3500])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "15600ad8e80a4c87aba6ca5566c7e318",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='t', max=3500.0, step=35.0), Output()), _dom_classes=…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<pybamm.plotting.quick_plot.QuickPlot at 0x7fd4e17c45b0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# plot some variables that depend on particle size\n",
    "output_variables = [\n",
    "    \"Negative particle surface concentration distribution [mol.m-3]\",\n",
    "    \"Positive particle surface concentration distribution [mol.m-3]\",\n",
    "    \"X-averaged negative particle surface concentration distribution [mol.m-3]\",\n",
    "    \"Negative area-weighted particle-size distribution [m-1]\",\n",
    "    \"Positive area-weighted particle-size distribution [m-1]\",\n",
    "    \"Voltage [V]\",\n",
    "]\n",
    "\n",
    "sim.plot(output_variables=output_variables)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Variables that depend on particle size have names that end in `\"distribution\"`, e.g. `\"Negative particle surface concentration distribution\"`. The same variables without the `\"distribution\"` have been averaged over particle size, and can be compared to the corresponding variable with the same name from other models that have a single particle size (e.g. SPM).\n",
    "\n",
    "The particle size distributions do not vary with $x$, so you can use the \"X-averaged\" versions to better visualize the discretized distribution in $R$ that PyBaMM uses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The discrete sizes or \"bins\" used\n",
    "R_p = sim.solution[\"Positive particle sizes [m]\"].entries[\n",
    "    :, 0, 0\n",
    "]  # const in the x and current collector direction\n",
    "R_n = sim.solution[\"Negative particle sizes [m]\"].entries[:, 0, 0]\n",
    "\n",
    "# The distributions (number, area, and volume-weighted)\n",
    "f_a_p = sim.solution[\n",
    "    \"X-averaged positive area-weighted particle-size distribution [m-1]\"\n",
    "].entries[:, 0]\n",
    "f_num_p = sim.solution[\n",
    "    \"X-averaged positive number-based particle-size distribution [m-1]\"\n",
    "].entries[:, 0]\n",
    "f_v_p = sim.solution[\n",
    "    \"X-averaged positive volume-weighted particle-size distribution [m-1]\"\n",
    "].entries[:, 0]\n",
    "f_a_n = sim.solution[\n",
    "    \"X-averaged negative area-weighted particle-size distribution [m-1]\"\n",
    "].entries[:, 0]\n",
    "f_num_n = sim.solution[\n",
    "    \"X-averaged negative number-based particle-size distribution [m-1]\"\n",
    "].entries[:, 0]\n",
    "f_v_n = sim.solution[\n",
    "    \"X-averaged negative volume-weighted particle-size distribution [m-1]\"\n",
    "].entries[:, 0]\n",
    "\n",
    "# plot\n",
    "f, axs = plt.subplots(1, 2, figsize=(10, 4))\n",
    "\n",
    "# negative electrode\n",
    "width_n = (R_n[-1] - R_n[-2]) / 1e-6\n",
    "axs[0].bar(\n",
    "    R_n / 1e-6,\n",
    "    f_a_n * 1e-6,\n",
    "    width=width_n,\n",
    "    alpha=0.3,\n",
    "    color=\"tab:blue\",\n",
    "    label=\"area-weighted\",\n",
    ")\n",
    "axs[0].bar(\n",
    "    R_n / 1e-6,\n",
    "    f_num_n * 1e-6,\n",
    "    width=width_n,\n",
    "    alpha=0.3,\n",
    "    color=\"tab:red\",\n",
    "    label=\"number-weighted\",\n",
    ")\n",
    "axs[0].bar(\n",
    "    R_n / 1e-6,\n",
    "    f_v_n * 1e-6,\n",
    "    width=width_n,\n",
    "    alpha=0.3,\n",
    "    color=\"tab:green\",\n",
    "    label=\"volume-weighted\",\n",
    ")\n",
    "axs[0].set_xlim((0, 25))\n",
    "axs[0].set_xlabel(\"Particle size $R_{\\mathrm{n}}$ [$\\mu$m]\", fontsize=12)\n",
    "axs[0].set_ylabel(\"[$\\mu$m$^{-1}$]\", fontsize=12)\n",
    "axs[0].legend(fontsize=10)\n",
    "axs[0].set_title(\"Discretized distributions (histograms) in negative electrode\")\n",
    "\n",
    "# positive electrode\n",
    "width_p = (R_p[-1] - R_p[-2]) / 1e-6\n",
    "axs[1].bar(\n",
    "    R_p / 1e-6,\n",
    "    f_a_p * 1e-6,\n",
    "    width=width_p,\n",
    "    alpha=0.3,\n",
    "    color=\"tab:blue\",\n",
    "    label=\"area-weighted\",\n",
    ")\n",
    "axs[1].bar(\n",
    "    R_p / 1e-6,\n",
    "    f_num_p * 1e-6,\n",
    "    width=width_p,\n",
    "    alpha=0.3,\n",
    "    color=\"tab:red\",\n",
    "    label=\"number-weighted\",\n",
    ")\n",
    "axs[1].bar(\n",
    "    R_p / 1e-6,\n",
    "    f_v_p * 1e-6,\n",
    "    width=width_p,\n",
    "    alpha=0.3,\n",
    "    color=\"tab:green\",\n",
    "    label=\"volume-weighted\",\n",
    ")\n",
    "axs[1].set_xlim((0, 25))\n",
    "axs[1].set_xlabel(\"Particle size $R_{\\mathrm{p}}$ [$\\mu$m]\", fontsize=12)\n",
    "axs[1].set_ylabel(\"[$\\mu$m$^{-1}$]\", fontsize=12)\n",
    "axs[1].set_title(\"Positive electrode\")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Custom size distributions"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we show how to change the distribution parameters, or set any distribution of choice. We will set the distribution parameters for the positive distribution (leaving the one for the negative electrode as the default lognormal). We refer to the [MPM notebook](https://github.com/pybamm-team/PyBaMM/blob/develop/docs/source/examples/notebooks/models/MPM.ipynb) for more examples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set the area-weighted mean radius to be the reference value from the parameter set\n",
    "R_av_p_dim = params[\"Positive particle radius [m]\"]\n",
    "\n",
    "# Standard deviation (dimensional)\n",
    "sd_p_dim = 0.6 * R_av_p_dim\n",
    "\n",
    "# Minimum and maximum particle sizes (dimensional)\n",
    "R_min_p = 0\n",
    "R_max_p = 3 * R_av_p_dim\n",
    "\n",
    "# Set the area-weighted particle-size distribution.\n",
    "# Choose a lognormal (but any pybamm function could be used)\n",
    "\n",
    "\n",
    "def f_a_dist_p_dim(R):\n",
    "    return pybamm.lognormal(R, R_av_p_dim, sd_p_dim)\n",
    "\n",
    "\n",
    "# Note: the only argument must be the particle size R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# input params to the dictionary\n",
    "distribution_params = {\n",
    "    \"Positive minimum particle radius [m]\": R_min_p,\n",
    "    \"Positive maximum particle radius [m]\": R_max_p,\n",
    "    \"Positive area-weighted \" + \"particle-size distribution [m-1]\": f_a_dist_p_dim,\n",
    "}\n",
    "params.update(distribution_params, check_already_exists=False)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solve and plot "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# load parameter values into simulation\n",
    "sim_custom = pybamm.Simulation(model, parameter_values=params)\n",
    "\n",
    "# solve\n",
    "sim_custom.solve(t_eval=[0, 3500])\n",
    "\n",
    "# plot\n",
    "output_variables = [\n",
    "    \"X-averaged negative area-weighted particle-size distribution [m-1]\",\n",
    "    \"X-averaged positive area-weighted particle-size distribution [m-1]\",\n",
    "    \"Voltage [V]\",\n",
    "]\n",
    "quickplot = pybamm.QuickPlot(\n",
    "    [sim, sim_custom],\n",
    "    output_variables=output_variables,\n",
    "    labels=[\"default lognormals\", \"custom\"],\n",
    ")\n",
    "quickplot.plot(0)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare MP-DFN to MPM and DFN models"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The MP-DFN is an extension of the MPM (size distributions, but no x variation) and DFN models (x variation, but no size distribution). Here we compare the three for the same parameter values, for a discharge followed by a relaxation. Note: this is implemented here by specifying the current function to be a Heaviside, not using the `Experiment` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "models = [\n",
    "    pybamm.lithium_ion.DFN(options={\"particle size\": \"distribution\"}, name=\"MP-DFN\"),\n",
    "    pybamm.lithium_ion.MPM(name=\"MPM\"),\n",
    "    pybamm.lithium_ion.DFN(name=\"DFN\"),\n",
    "]\n",
    "\n",
    "# parameters\n",
    "params = pybamm.ParameterValues(\"Marquis2019\")\n",
    "params = pybamm.get_size_distribution_parameters(params)\n",
    "\n",
    "# experiment\n",
    "experiment = pybamm.Experiment(\n",
    "    [\n",
    "        \"Discharge at 1C for 3450 seconds\",\n",
    "        \"Rest for 3600 seconds\",\n",
    "    ]\n",
    ")\n",
    "\n",
    "\n",
    "# solve\n",
    "sims = []\n",
    "for model in models:\n",
    "    sim = pybamm.Simulation(model, parameter_values=params, experiment=experiment)\n",
    "    sim.solve()\n",
    "    sims.append(sim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot current, voltage\n",
    "qp = pybamm.QuickPlot(sims, output_variables=[\"Current [A]\", \"Voltage [V]\"])\n",
    "qp.plot(0)"
   ]
  },
  {
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    "During discharge, the MPM overpredicts the voltage since it neglects the transport (and therefore resistances) through the electrolyte. During the relaxation portion, the DFN overpredicts the rate of relaxation to equilibrium compared to the MP-DFN and MPM. However, the slower relaxation of the size distribution models has been shown to agree better with experiment [[5]](#References)."
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    "## References\n",
    "\n",
    "The relevant papers for this notebook are:"
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      "[1] Joel A. E. Andersson, Joris Gillis, Greg Horn, James B. Rawlings, and Moritz Diehl. CasADi – A software framework for nonlinear optimization and optimal control. Mathematical Programming Computation, 11(1):1–36, 2019. doi:10.1007/s12532-018-0139-4.\n",
      "[2] Marc Doyle, Thomas F. Fuller, and John Newman. Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell. Journal of the Electrochemical society, 140(6):1526–1533, 1993. doi:10.1149/1.2221597.\n",
      "[3] Charles R. Harris, K. Jarrod Millman, Stéfan J. van der Walt, Ralf Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, Julian Taylor, Sebastian Berg, Nathaniel J. Smith, and others. Array programming with NumPy. Nature, 585(7825):357–362, 2020. doi:10.1038/s41586-020-2649-2.\n",
      "[4] Toby L. Kirk, Jack Evans, Colin P. Please, and S. Jonathan Chapman. Modelling electrode heterogeneity in lithium-ion batteries: unimodal and bimodal particle-size distributions. arXiv:2006.12208, 2020. URL: https://arxiv.org/abs/2006.12208, arXiv:2006.12208.\n",
      "[5] Toby L. Kirk, Colin P. Please, and S. Jon Chapman. Physical modelling of the slow voltage relaxation phenomenon in lithium-ion batteries. Journal of The Electrochemical Society, 168(6):060554, jun 2021. URL: https://doi.org/10.1149/1945-7111/ac0bf7, doi:10.1149/1945-7111/ac0bf7.\n",
      "[6] Scott G. Marquis, Valentin Sulzer, Robert Timms, Colin P. Please, and S. Jon Chapman. An asymptotic derivation of a single particle model with electrolyte. Journal of The Electrochemical Society, 166(15):A3693–A3706, 2019. doi:10.1149/2.0341915jes.\n",
      "[7] Valentin Sulzer, Scott G. Marquis, Robert Timms, Martin Robinson, and S. Jon Chapman. Python Battery Mathematical Modelling (PyBaMM). Journal of Open Research Software, 9(1):14, 2021. doi:10.5334/jors.309.\n",
      "\n"
     ]
    }
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   "source": [
    "pybamm.print_citations()"
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